If you're only using three at a time, you could always do this:

sub is_ok
{
        $_[0][0] != $_[1][0] &&
        $_[0][0] != $_[1][1] &&
        $_[0][0] != $_[1][2] &&
        $_[0][1] != $_[1][0] &&
        $_[0][1] != $_[1][1] &&
        $_[0][1] != $_[1][2] &&
        $_[0][2] != $_[1][0] &&
        $_[0][2] != $_[1][1] &&
        $_[0][2] != $_[1][2];
}
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Very rudimentary, but at the same time, this "unrolled" version is way faster than any list or hash based operation. Using a quick Benchmark test, it was 80% faster than other bits posted here.